Explain why x4 16 has two real solutions while x3 8 has only one real solution?
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Assuming you mean x^4 = 16 (x to the power of 4 equals 16)and
x^3 = 8 (x to the power of 3 equals 8).
When the power is even and the right side is positive, a
solution can be negative since the 2 negatives will cancel out. For
any even power, it's just an extension of that, they will cancel
out in pairs. For an odd power, a negative solution would give you
a negative right side so it must be positive.
Thus, in x^4=16, x can be either 2 or -2 but in x^3 = 8, x can
only be 2.